Title: Distributionally Robust Optimization: Expectation Shortfall and k-sum problem
Speaker: Dr. Anulekha Dhara, Research Fellow at University of Michigan
Venue: Seminar Room, IEOR (2nd floor)
Time and Date: 11:30 am, 9th October
Abstract: In a deterministic optimization model, the input parameters are taken to be known exactly/fixed. This need not be the case in real-world problems where the input parameters may not take a fixed value or may depend on some random variable. The standard optimization theory involving the well-known Karush-Kuhn-Tucker conditions need not be directly applicable to such situations.To deal with the uncertainty in data, two approaches have come into existence, namely stochastic optimization and robust optimization. In case of stochastic optimization, the parameters are assumed to follow some known distribution with the goal of optimizing the expected cost while in robust optimization, the data belongs to an uncertainty or ambiguity set with the aim of optimizing the worst-case cost.
In this talk, I shall present two problems involving a special form of robust optimization, namely distributionally robust optimization wherein the uncertainty set considered are defined by a class of probability distributions satisfying marginal and/or moment information. The first problem discusses the worst-case bound for expected shortfall which is “close” to a reference marginal information where closeness in distance among distributions is measured using φ-divergence while the second problem deals with solvability of distributionally robust k-sum optimization problem.
Bio: Dr. Anulekha Dhara is currently a Research Fellow at University of Michigan applying optimization tools to power systems. Prior to this, she has been a postdoc in Engineering Systems and Design pillar at Singapore University of Technology and Design. She has been an Assistant Professor at IIT Gandhinagar from 2011-2014. She obtained her B.Sc. from University of Delhi and M.Sc. and Ph.D. from IIT Delhi. Her primary area of research is robust optimization. She also has expertise in nonconvex nonsmooth optimization.